The presence of dxz−dyz orbital ordering is often considered a hallmark of the nematic phase of Fe-based superconductors, including FeSe, but the details of the order parameter remain controversial. Here, we report a high-resolution angle-resolved photoemission spectroscopy study of single crystals of FeSe, accounting for the photon-energy dependence and making a detailed analysis of the temperature dependence. We find that the hole pocket undergoes a fourfold-symmetry-breaking distortion in the nematic phase below 90 K, but, in contrast, the changes to the electron pockets do not require fourfold symmetry breaking. Instead, there is an additional separation of the existing dxy and dxz/yz bands, which themselves are not split within resolution. These observations lead us to propose a scenario of “unidirectional nematic bond ordering” to describe the low-temperature electronic structure of FeSe, supported by good agreement with ten-orbital tight-binding model calculations.